In a club of 35 boys and 28 girls, 80% of the boys and 25% of the girls have been members for more than 2 years. If n percent of the club have been members for more than 2 years, what is the value of n?

Answer

To find the percentage \( n \) of club members who have been members for more than 2 years, we will follow these steps:

### Step 1: Calculate the number of boys who have been members for more than 2 years.
We know there are 35 boys in total and 80% of them have been members for more than 2 years.

\[ \text{Number of boys} = 35 \]
\[ \text{Percentage of boys} = 80\% = \frac{80}{100} = 0.8 \]
\[ \text{Boys who have been members for more than 2 years} = 0.8 \times 35 = 28 \]

### Step 2: Calculate the number of girls who have been members for more than 2 years.
There are 28 girls in total and 25% of them have been members for more than 2 years.

\[ \text{Number of girls} = 28 \]
\[ \text{Percentage of girls} = 25\% = \frac{25}{100} = 0.25 \]
\[ \text{Girls who have been members for more than 2 years} = 0.25 \times 28 = 7 \]

### Step 3: Calculate the total number of members who have been members for more than 2 years.
Now, we add the number of boys and girls who have been members for more than 2 years.

\[ \text{Total members who have been members for more than 2 years} = 28 + 7 = 35 \]

### Step 4: Calculate the total number of members in the club.
The total number of members in the club is the sum of boys and girls.

\[ \text{Total members} = 35 + 28 = 63 \]

### Step 5: Calculate the percentage \( n \) of members who have been members for more than 2 years.
Now, we calculate the percentage of members who have been members for more than 2 years.

\[ n = \left( \frac{\text{Total members who have been members for more than 2 years}}{\text{Total members}} \right) \times 100 \]
\[ n = \left( \frac{35}{63} \right) \times 100 \]

### Step 6: Simplify the fraction and calculate \( n \).
We simplify \( \frac{35}{63} \):

\[ \frac{35}{63} = \frac{5}{9} \quad \text{(dividing both numerator and denominator by 7)} \]

Now, calculate \( n \):

\[ n = \left( \frac{5}{9} \right) \times 100 \approx 55.56\% \]

Thus, the value of \( n \) is approximately \( 55.56\% \).

### Summary of Steps:
1. Calculate the number of boys who have been members for more than 2 years.
2. Calculate the number of girls who have been members for more than 2 years.
3. Add the boys and girls to find the total number of members who have been members for more than 2 years.
4. Find the total number of members in the club.
5. Calculate the percentage of members who have been members for more than 2 years.